A town has a population of 2000 people at time t = 0.

In each of the following cases, write a formula for the population, P, of the town as a function of year t.
(a) The population increases by 60 people per year.

I thought it would be P= 2000 (1.03)^t

(b) The population increases by 5% per year.

I thought it would be P = 2000 (.95)^t

(1) 60 is just a number, not a percentage

P = 2000 + 60t

(2) P is increasing, so you want

P = 2000 * 1.05^t

0.95^t means that each year the population decreases by 5%

Well, you're a bit off with both of your formulas there, my friend. But don't worry, I'm here to help you out with a little clown wisdom!

(a) If the population increases by 60 people per year, we can start by saying that the population at time t = 0 is 2000. Then, for every year that passes, we add 60 people to that initial population. So the correct formula would be P = 2000 + 60t. See, it's as simple as adding a little something extra each year, just like adding extra sprinkles on top of your ice cream!

(b) Now, if the population increases by 5% per year, we need to use a different approach. We can say that the initial population at time t = 0 is 2000, and then for every year that goes by, the population increases by 5% of its current value. Mathematically, we can express this as P = 2000 * (1 + 0.05)^t. Isn't that formula a bit sneaky? It keeps multiplying itself by a tiny bit each year, just like a snowball rolling down a hill, getting bigger and bigger!

So there you have it, my friend. Two formulas that'll help you understand how the population of that town changes over time. Just remember, always have a little fun when you're crunching those numbers!

For case (a) where the population increases by 60 people per year, the correct formula for the population, P, of the town as a function of year t would be:

P = 2000 + 60t

Here, 2000 represents the initial population at t = 0, and 60t represents the increase in population of 60 people per year, multiplied by the number of years, t.

For case (b) where the population increases by 5% per year, the correct formula for the population, P, of the town as a function of year t would be:

P = 2000 * (1 + 0.05)^t

Here, 2000 represents the initial population at t = 0, and (1 + 0.05)^t represents the increase in population of 5% per year, compounded annually, raised to the power of the number of years, t.

In order to determine the correct formula for the population, we need to consider the given information and analyze the situation.

(a) The population increases by 60 people per year.
To find the formula for the population, we need to consider that each year, the population increases by a fixed amount of 60 people. This means that at any given time t, the population P can be obtained by adding 60 for each year that has passed since t = 0. So, the correct formula would be:

P = 2000 + 60t

Here, t represents the number of years that have passed since t = 0, and P represents the population at that time.

(b) The population increases by 5% per year.
To find the formula for the population, we need to consider that each year, the population increases by a percentage of its current value. In this case, the population is growing by 5% per year. To calculate the total population each year, we multiply the previous year's population by 1 plus the growth rate (in decimal form). So, the correct formula would be:

P = 2000(1 + 0.05)^t

Here, t represents the number of years that have passed since t = 0, and P represents the population at that time.

Thank you so much for all of your help!